PIEAS Admission Test (BS, MS and PhD)

Question 1

What is the derivative of f(x) = e^(2x) * sin(3x) with respect to x?

Accepted Answer

e^(2x) (2sin(3x) + 3cos(3x))

Answer

e^(2x) (3sin(3x) + 2cos(3x))

Answer

2e^(2x) * sin(3x) + 3e^(2x) * cos(3x)

Answer

e^(2x) (2cos(3x) + 3sin(3x))

Question 2

What is the value of the integral of (2x + 3) dx from 0 to 2?

Accepted Answer

10

Answer

4

Answer

6

Answer

8

Question 3

For a matrix A, if det(A) = 0, what does it imply about the matrix?

Accepted Answer

It is singular

Answer

It is identity

Answer

It is invertible

Answer

It is symmetric

Question 4

What is the limit of (sin(x)/x) as x approaches 0?

Accepted Answer

1

Answer

0

Answer

Infinity

Answer

-1

Question 5

If y = ln(x^2), what is dy/dx?

Accepted Answer

2/x

Answer

1/x

Answer

x^2

Answer

2ln(x)

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